Is Aunt Petunia a Squib?
Good question. No, she is not, but — [Laughter]. No, she is not a Squib. She is a Muggle, but — [Laughter]. You will have to read the other books. You might have got the impression that there is a little bit more to Aunt Petunia than meets the eye, and you will find out what it is. She is not a squib, although that is a very good guess. Oh, I am giving a lot away here. I am being shockingly indiscreet.
This would also explain why the information about teachers' spouses has been restricted so far.
A few of the Hogwarts professors have spouses, but the information is restricted – we’ll find out why!
Here are a few of the main objections to this theory:
1. But Hermione took Muggle Studies and saw Aunt Petunia on the platform at the end of OotP. Surely she would have recognized her and said something to Harry?
Not if Dumbledore made her promise not to. She kept stuff from Harry at the beginning of OotP for the same reason.
2. Muggles can't see Hogwarts.
Q: Can Muggles see Hogwarts ? (Melinda, 11, CA)
A: Aaah — who asked that? Smart Melinda! You find out in Book 4. When they look towards it, as a safety precaution, they see a ruin with a sign saying it's unsafe ... they mustn't enter. They can't see it as it really is.
Nothing on what happens if they ignore the sign and enter anyway.
3. Aunt Petunia hates magic.
Well Harry certainly thinks so, but Harry's not always right about people. She does seem afraid of it (what Muggle wouldn't be?), which would make it extremely brave of her to teach at Hogwarts anyway. Then again, she is Lily Evans's sister, so maybe she's a lot braver than we all thought.
4. What about Uncle Vernon?
Maybe he thinks she teaches at an ordinary Muggle boarding school during the year. I always thought it was a bit suspicious that, except for OotP, he's the only one ever mentioned as showing up at the station to collect Harry at the end of the year....
5. Wouldn't Harry see her at meals?
Maybe she prefers to dine alone in her room, as much out of the company of wizard's as possible.
6. But why bother? What would be the point of going through all that trouble to have her be the Muggle Studies teacher?
The blood protection. As long as Harry can call home the place where his mother's blood dwells, there Voldemort cannot hurt him. Harry certainly thinks of Hogwarts as his home, much more than Privet Drive, and if Aunt Petunia is teaching there, it's her second home too. This would mean that Harry is protected both in the castle and at Privet Drive, and would help explain why Dumbledore is willing to let him face Voldemort at school his first year.
"D'you think he meant you to do it?" said Ron. "Sending you your father's cloak and everything?"
"Well," Hermione exploded, "if he did — I mean to say — that's terrible — you could have been killed."
"No, it isn't," said Harry thoughtfully. "He's a funny man, Dumbledore. I think he sort of wanted to give me a chance. I think he knows more or less everything that goes on here, you know. I reckon he had a pretty good idea we were going to try, and instead of stopping us, he just taught us enough to help. I don't think it was an accident he let me find out how the mirror worked. It's almost like he thought I had the right to face Voldemort if I could...."
PS/SS, p. 302
If I were Dumbledore, I would feel a lot more comfortable letting a first year do this if I knew Voldemort couldn't harm him because Aunt Petunia was living in the castle. And when Harry asks why Quirrell couldn't touch him, Dumbledore explains it was because of Lily's sacrifice — the same magic he used to protect Privet Drive.
Harry also faced Voldemort at school his second year and got away; in his fourth year, Voldemort did get his hands on him, but had to take him away from the castle to do it; his fifth year Voldemort got into his mind to show him visions, but couldn't harm him by, say, having him drink poison or throw himself down the stairs; and Voldemort didn't even try breaking into the castle sixth year, even though Dumbledore was gone for long stretches of time. Maybe Harry has been safe at school all this time because Lily's blood dwells in the castle too.